EXHIBIT 31.1

CERTIFICATION

I, Adelene Q. Perkins, certify that:

1. I have reviewed this annual report on Form 10-K of Infinity Pharmaceuticals, Inc. (the Registrant);

2. Based on my knowledge, this annual report does not contain any untrue statement of a material fact or omit to state a material fact
necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this annual report;

3. Based on my knowledge, the financial statements, and other financial information included in this annual report, fairly present in all
material respects the financial condition, results of operations and cash flows of the Registrant as of, and for, the periods presented in this annual report;

4. I am responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as
defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the Registrant and have:

(a) designed such
disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under my supervision, to ensure that material information relating to the Registrant, including its consolidated subsidiaries, is made known to me
by others within those entities, particularly during the period in which this annual report is being prepared;

(b) designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under my supervision, to provide reasonable assurance regarding the reliability of financial reporting and
the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

(c) evaluated the effectiveness of the Registrants disclosure controls and procedures and presented in this annual report my conclusions about the effectiveness of the disclosure controls and
procedures, as of the end of the period covered by this annual report based on such evaluation; and

(d)
disclosed in this annual report any change in the Registrants internal control over financial reporting that occurred during the Registrants fourth fiscal quarter that has materially affected, or is reasonably likely to materially
affect, the Registrants internal control over financial reporting; and

5. I have disclosed, based on my most recent
evaluation of internal control over financial reporting, to the Registrants auditors and the audit committee of the Registrants board of directors (or persons performing the equivalent functions):

(a) all significant deficiencies and material weaknesses in the design or operation of internal control over financial
reporting which are reasonably likely to adversely affect the Registrants ability to record, process, summarize and report financial information; and

(b) any fraud, whether or not material, that involves management or other employees who have a significant role in the Registrants internal control over financial reporting.



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|Date: March 12, 2010 |  |  |  | /s/    ADELENE Q. PERKINS                                                                                             
|                     |  |  |  | Adelene Q. Perkins President and Chief Executive Officer (Principal Executive
Officer and Principal Financial Officer)